Of course they are. That is the price they pay for enjoying the extra business that the Olympics bring in each time they are held in a city. If the city does not want to be responsible, then do not invite them into your city. It's not like they invaded.
The Olympics requires new construction of stadiums and equipment and increased infrastructure to handle the crowds. After the games, new buildings are rarely used. The temporary boost in tourism from the games does not cover the costs of having to maintain unneeded structures after the games. There should be stricter requirements for the games, such as having Olympic-quality sporting arenas already in place.
I believe that host Olympic cities do always struggle with how to deal with what comes after the games. Hosting the Olympics is a huge honor, but it also comes at a huge cost. Once the games are finished, each host city must deal with the mess that both spectators and athletes have left behind, from deciding how to use empty stadiums (if at all), to cleaning up debris.
I do think that host Olympic cities are often left with a mess of trash and waste spread throughout their communities. The Olympic committee is there to put on the games and after years of work are eager to leave immediately after the games. More can be done to help these cities get back to normal life.
Host cities and their affiliates have great venues after the Olympics have cleared. Sure I agree that host cities do have to deal with excess in garbage/recycling however that simply teaches the host city how to deal with operate those services more efficiently. The great stadiums/velodromes/athletes villages etc become usable sporting facilities after the games. The athletes villages in some cases have turned into low cost housing or student housing. Hosting the Olympics is a huge honor, the cost is huge. However once the games are finished, each host city needs to follow through with plans of use!